A Simple Model for the Formation of Step-Free Surfaces
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A Simple Model for the Formation of Step-Free Surfaces Kee-Chul Chang and Jack M. Blakely Dept. of Materials Science and Engineering, Cornell University, Ithaca, NY 14850, USA ABSTRACT Arrays of step-free regions on the surface of silicon have been created either by evaporating atoms from craters[1] or by depositing atoms on mesas[2]. In most cases the maximum extent of the step-free regions is limited by the occurrence of circular pits or islands in the crater or mesa structures. We model the process of step clearing and nucleation of these pits and islands by approximating the initial surface by an array of circular steps whose movement is mediated by adatoms. BCF (Burton-Cabrera-Frank) theory[3] is used to incorporate the effects of surface diffusion, evaporation and the deposition of atoms on the surface. We include the effects of step curvature and step interactions. If the step spacing is large enough, we find that the innermost step moves outwards to create a step-free region; otherwise it moves inward and leads to large scale smoothening of the surface. Pit or island nucleation in the center of the craters or mesas is also included in the model by using classical nucleation theory. We investigate the effect of deposition flux and temperature on the formation of step-free surfaces and compare the results to reported experiments on silicon and to some of our recent work on sapphire. INTRODUCTION Although we have a mature wafer processing technology which commonly produces wafers with RMS roughness of several angstroms and a miscut of 0.1 degrees, it is not yet possible to make wafers with no miscut and no atomic steps on their surfaces. Step-free surfaces may be beneficial for a variety of applications for which it will usually be sufficient to create step-free regions (at the expense of other regions with high concentration of steps) and selectively make devices on those step-free regions. Fairly large step-free regions can result from spontaneous step bunching[4]. However there is no way to know in advance which regions will be step-free, so characterization of the surface is needed after the processing. The method that our group[5] and several other groups[6,7] are pursuing, is to use ‘assisted’ self assembly to get large step-free regions at predetermined locations. The surface is first patterned to create regular arrays of craters or mesas and this is eventually followed by high temperature annealing to produce sublimation or deposition. Most of the experiments in the field have been on Si(111) and (100) surfaces by using a trial and error approach to determine the optimum processing conditions. Experiments by our group have demonstrated that it is possible to get large (up to 50 x 50 µm) step-free areas on silicon by patterning and annealing. The experiments also show that the extent of the step-free regions may be limited by the appearance of pits (or islands in the growth case). An illustration of the patterns and the atomic processes that lead the step clearing is shown in figure 1.
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